US President Barack Obama is expected to announce that he is grounding plans to return astronauts to the moon.
The decision is set to be revealed as part of Mr Obama's budget plan for 2011.
It follows the recommendations of an independent commission set up to assess the future of human space flight.
It is expected that Nasa will be given £3.75bn ($6bn) extra funding over the next five years but told to take a new direction.
The focus will be on encouraging commercial spaceship development, extending the life of the International Space Station and working on a "flexible path" for human space exploration.
Experts say this may include trips to a nearby asteroid, a Martian moon or a brief visit to the Earth's moon.
But it rules out Nasa's plan for regular flights to the moon and the setting up of a permanent base there by the end of the decade.
I don't think this country is ready to abandon human space flight, nor should it.
Former astronaut Leroy Chiao
The Constellation Programme was initiated by former president George W Bush and has already cost £5.7bn ($9.1bn).
But it started to unravel when promised budget increases did not materialise.
"Constellation is dead," a White House official has said.
The cost of space exploration has become a major factor as the US grapples with the continuing financial crisis.
But the threat of cutbacks has angered people living in communities like Houston, in Texas, that rely on the space industry.
Rick Perry, Republican Governor of Texas, said: "I'm not saying Nasa needs to sacred cow and 'Hands Off'. But I could find lots of money that has been spent in special interests that didn't do a cotton-picking thing for the Texas economy."
Neil Armstrong was the first man to walk on the moon
On Friday, Mr Obama honoured astronauts who had died in the Apollo 1, Challenger and Columbia space missions.
He said: "All of humanity has benefited from their courage and devotion.
"We mourn their loss while celebrating their spirit of discovery. May their sacrifice be an inspiration as we continue our nation's work to explore our universe."
But former astronaut Leroy Chiao, who was a member of the President's Augustine Commission, said sending astronauts into space is still important to Americans.
"It is difficult to predict the future. I'm cautiously optimistic. I don't think this country is ready to abandon human space flight, nor should it. I think we have to be realistic about the budget," he said.
"If Nasa's budget is going to more or less remain flat for the next few years, then we cannot sustain what's been going on.
"And so the Constellation Programme will have to be adjusted. Something will have to change."